Hi Emily,
Everything you said during that explanation was correct, besides the assumption you made that as temperature increases, the sum of pH + pOH will still equal 14.
The sum of pH + pOH will be whatever the -log(Kw) is and therefore will change will the changing temperature.
So you are right that the pH and pOH both decrease, and both decrease by the same amount, but they will sum to a new value now.